Let $s(n)$ denote the number of distinct crystallographic groups in $Isom(\mathbb{R}^n)$.
Apparently the best known upper bound so far is
$$
s(n)\le e^{e^{4n^2}},
$$
given by Peter Buser in $1985$. On ...

Recall that a Weil algebra is a finite-dimensional real unital algebra that admits exactly one homomorphism to R.
Such algebras form the basis of the Weil approach to differential geometry, pioneered ...

Let $K \subset L$ be a finite Galois extension, $\sigma$ an automorphism of $L$ (not necessarily fixing $K$) and let $E$ be a finite-dimensional vector space over $L$ together with an $\sigma$-linear ...

In his papers "Isocrystals with additional structure" I and II, Kottwitz defines the notion of $\sigma$-$L$-spaces. In the first one the situation is the following
$k$ an algebraically closed field ...

Is there a mathematical theory that explains the shape of a snowflake? Why is it not round?
Update Tree-like metric spaces appear often as limits of sequences of metric spaces (say, asymptotic cones ...

I am seeking references for precise statements and rigorous proofs of some facts about the actions of quantum root vectors and $R$-matrices on crystal bases for finite-dimensional representations of ...

In his paper "Generic Galois Theory of Local Rings", G.C. Wraith states on p. 743 that the (big) crystalline topos "can be conveniently described in terms of the theory it describes". What exactly is ...

If you want to compute crystalline cohomology of a smooth proper variety $X$ over a perfect field $k$ of characteristic $p$, the first thing you might want to try is to lift $X$ to the Witt ring $W_k$ ...

I am trying to understand some construction done by Lusztig in his book on quantum groups. Given some Cartan datum, let $U=U_q(\mathfrak{g})$ the standard quantized enveloping algebra of the Kac-Moody ...